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We present nuclear spectral energy distributions (SEDs) in the range 0.4-16micron for an expanded CfA sample of Seyfert galaxies. The spectral indices from 1-16micron range from alpha_IR 0.9 to 3.8. The shapes of the spectra are correlated with Seyfert type in the sense that steeper nuclear SEDs (nu*f_nu increasing with increasing wavelength) tend to be found in Seyfert 2s and flatter SEDs (nu *f_nu constant) in Seyfert 1-1.5s. The galaxies optically classified as Seyferts 1.8s and 1.9s display values of alpha_IR as in type 1 objects, or values intermediate between those of Seyfert 1s and Seyfert 2s. The intermediate SEDs of many Seyfert 1.8-1.9s may be consistent with the presence of a pure Seyfert 1 viewed through a moderate amount (A_V <5mag) of foreground galaxy extinction. We find, however, that between 10 and 20% of galaxies with broad optical line components have steep infrared SEDs. Torus models usually adopt high equatorial opacities to reproduce the infrared properties of Seyfert 1s and 2s, resulting in a dichotomy of infrared SEDs (flat for type 1s, and steep for type 2s). Such a dichotomy, however, is not observed in our sample. The wide range of spectral indices observed in the type 2 objects, the lack of extremely steep SEDs, and the large numbers of objects with intermediate spectral indices cannot be reconciled with predictions from existing optically thick torus models. We discuss possible modifications to improve torus models, including low optical depth tori, clumpy dusty tori, and high-optical-depth tori with an extended optically thin component.